Internal problem ID [15279]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 509.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+6*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (\frac {1}{120} x^{5}+c_{1} +c_{2} x +c_{3} x^{2}+c_{4} x^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 39
DSolve[y''''[x]-4*y'''[x]+6*y''[x]-4*y'[x]+y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{120} e^x \left (x^5+120 c_4 x^3+120 c_3 x^2+120 c_2 x+120 c_1\right ) \]